A knife or scalpel which is composed of a gripping handle and a blade adapted to be detachably mounted on the gripping handle at an end has been hitherto known. To this end, the blade has a profiled slot formed therein, while the handle has a blade mounting extension or projection of such a profile that a projection can be easily received in the profiled slot and brought to the closely engaging position by appropriately displacing the blade relative to the mounting projection. The hitherto known knife however suffers from the drawback that it is difficult to support the blade firmly by means of the mounting projection without any looseness, because of, for example, the inevitable tolerance that exists in the geometrical configurations of the mounting extension and the slot which are engaged with each other. Such drawback can become serious, particularly in the case of a surgeon's knife, or scalpel.